TI84 Plus and Casio
Prizm: Area between Polynomials p(x) and
q(x)
The program
POLYSURF calculates the area of a surfaces with:
* Side borders
are straight vertical lines. The left
border line begins at x = 0
* The top and
the bottom are defined polynomials: p(x) for the top and q(x) for the bottom.
* There are n
partitions in the shape, for all partition points, p(x) > q(x).
The program also
draws the shape. If the number of
partitions are 4 or less, an exact area is calculated. Otherwise, p(x) and q(x) are approximated by
a quartic polynomial and an approximated area is calculated.
TI84 Plus Program
POLYSURF
"EWS 20161206"
Disp "P(X) >
Q(X)"
FnOff
PlotsOff
{0}→L₁
Input
"P(0)=",P
{P}→L₂
Input
"Q(0)=",Q
{Q}→L₃
Input "NO. OF
PARTITIONS:",N
For(I,1,N)
ClrHome
Output(7,1,"POINT")
Output(7,8,I)
Output(8,1,"P(X)>Q(X)")
Input
"X:",X
Input
"P(X):",P
Input
"Q(X):",Q
augment(L₁,{X})→L₁
augment(L₂,{P})→L₂
augment(L₃,{Q})→L₃
End
L₁(dim(L₁))→L
If N=1
Then
LinReg(ax+b) L₁,L₂,Y₁
LinReg(ax+b) L₁,L₃,Y₂
End
If N=2
Then
QuadReg L₁,L₂,Y₁
QuadReg L₁,L₃,Y₂
End
If N=3
Then
CubicReg L₁,L₂,Y₁
CubicReg L₁,L₃,Y₂
End
If N≥4
Then
QuartReg L₁,L₂,Y₁
QuartReg L₁,L₃,Y₂
End
FnOn 1,2
fnInt(Y₁Y₂,X,0,L)→S
Disp "AREA=",S
Pause
ClrDraw
.5→Xmin
L+.5→Xmax
min(L₃).5→Ymin
max(L₂)+.5→Ymax
Shade(Y₂,Y₁,0,L)
Casio Prizm Program: POLYSURF
The character #
can be found by exiting to the “main” program menu (TOP, BOTTOM, etc). Press F6 for CHAR, select #, and press [EXE].
Get the
regressions by pressing [F4] (MENU), [F1] (STAT), [F6] twice (CALC, >) and
selecting the regression. The statistic variables a, b, c, d, and e
are calculated after regression calculation.
“EWS 20161206”
“P(x)>Q(x)”
{0} → List 1
“P(0)=”? → P
{P} → List 2
“Q(0)=”? → Q
{Q} → List 3
“# PARTITIONS:”? → N
For 1 → I To N
“POINT”
I ◢
“X:”? → X
“P(X):”? → P
“Q(X):”? → Q
Augment(List 1, {X})
→ List 1
Augment(List 2, {P})
→ List 2
Augment(List 3, {Q})
→ List 3
Next
If N = 1
Then
LinearReg (ax+b)
List 1, List 2
a → A
b → B
“Ax+B” → Y1
LinearReg (ax+b)
List 1, List 3
a → F
b → G
“Fx+G” → Y2
IfEnd
If N = 2
Then
QuadReg List 1, List
2
a → A
b → B
c → C
“Ax^2+Bx+C” → Y1
QuadReg List 1, List
3
a → F
b → G
c → H
“Fx^2+Gx+H” → Y2
IfEnd
If N = 3
Then
CubicReg List 1,
List 2
a → A
b → B
c → C
d → D
“Ax^3+Bx^2+Cx+D” → Y1
CubicReg List 1,
List 3
a → F
b → G
c → H
d → I
“Fx^3+Gx^2+Hx+I” → Y2
IfEnd
If N ≥ 4
Then
QuartReg List 1,
List 2
a → A
b → B
c → C
d → D
e → E
“Ax^4+Bx^3+Cx^2+Dx+E”
→ Y1
CubicReg List 1,
List 3
a → F
b → G
c → H
d → I
e → J
“Fx^4+Gx^3+Hx^2+Ix+J”
→ Y2
IfEnd
List 1[Dim List 1] →
L
∫(Y1Y2, 0, L) → S
“AREA=”
S ◢
ClrGraph
ViewWindow .5,
L+.5, 1, Min(List 3).5, Max(List 2)+.5, 1
FLine 0, List 2[1],
0, List 1[3]
Dim List 1 → Z
Fline List 1[Z],
List 2[Z], List 1[Z], List 3[Z]
DrawGraph
Examples
Example 1
Data:
n

x

p(x)

q(x)

0

0

2

2

1

1

5

2

2

2

2

2

Number of
partitions, n = 2
Area = 12
Example 2
Data:
n

x

p(x)

q(x)

0

0.0

0.00

0.00

1

1.5

5.62

0.64

2

2.5

3.83

1.38

3

3.5

1.25

0.76

Number of
Partitions, n = 3
Area ≈ 13.16619792
Example 3
Data:
n

x

p(x)

q(x)

0

0.00

3.00

3.00

1

0.50

2.54

2.84

2

1.25

2.01

3.00

3

1.60

2.36

3.55

4

2.00

2.76

1.98

Number of
Partitions, n = 4
Area ≈ 10.77281698
This blog is
property of Edward Shore, 2016